高瀬正仁 著 『無限解析のはじまり ～ わたしのオイラー』 ちくま学芸文庫(２００９年）は、数学者レオンハルト・オイラー(1707～1783）の業績、足跡を辿る本です。膨大な資料の紹介がなされていますので、ウェブで参照できるものに関しては、リンクを紹介したいと思います。
オイラーは、ヨハン・ベルヌーイ（1667~1748）から数学を学んだそうです。オイラーが残した文献は800を越えるそうで(Original Documents (843))、オイラー全集の刊行がビルクホイザー（Birkhäuser）社によって1911年から始まったにもかかわらず現在なお未完結とのこと。
（http://eulerarchive.maa.org//enestrom.php?topic=avail&lang=e）
| 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 |
| 17 | The Art of Reckoning |
| 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 |
| 22 | On the communication of motion in collisions |
| 23 | On rectifiable algebraic curves |
| 24 | Solution of a remarkable case concerning tautochronism |
| 25 | A general method for summing series |
| 26 | Observations on a theory of Fermat and others on looking at prime numbers |
| 27 | On isoperimetric problems in the widest sense |
| 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 axn dx = dy + y2 dx |
| 33 | An attempt at a new theory of music, exposed in all clearness, according to the most well-founded principles of harmony |
| 34 | Dissertation on fire |
| 36 | Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders |
| 37 | On the motion of planets and orbits |
| 38 | Determination of orbits around the sun |
| 39 | Solution to a problem concerning astronomy |
| 40 | On the smallest oscillations of rigid and flexible bodies. A new and easy method. |
| 41 | On the sums of series of reciprocals |
| 42 | On the curve of fastest descent in whatever resistent medium |
| 43 | On harmonic progressions |
| 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 |
| 48 | Investigation of pairs of curves whose arcs that correspond to the same abscissa constitute an algebraic sum |
| 49 | On the oscillations of a flexible wire weighted with arbitrarily many little weights (?) |
| 50 | A method for computing the equation of a meridian |
| 51 | On the construction of equations using dragged motion, and of other things pertinent to the inverse method of tangents |
| 52 | Solution of a problem requiring the rectification of an ellipse |
| 53 | The solution of a problem relating to the geometry of position |
| 54 | A proof of certain theorems regarding prime numbers |
| 55 | Universal method for summation of series, further developed |
| 56 | New and easy method of finding curves enjoying a maximal or minimal property |
| 57 | A physical inquiry into the cause of the ebb and flow of the sea |
| 58 | Determination of the motion of a comet which can be observed in March of this year, 1742 |
| 59 | Theorems concerning the reduction of integral formulas to the quadrature of the circle |
| 60 | On the resolution of an integral, if after integration the value for the determined variable quantity is assigned |
| 61 | On sums of series of reciprocals from powers of natural numbers from another discussion, in which the sums are derived principally from another source |
| 62 | On the integration of differential equations of various degrees |
| 63 | Demonstration of the sum of the series 1 + 1/4 + 1/9 + 1/16 � |
| 64 | Leonhardus Eulerus mathematicus acutissimus ad auctorem |
| 65 | A method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense |
| 66 | Theory of the motions of planets and comets |
| 69 | On the imparting of motion from a collision of bodies not striking each other directly |
| 70 | On the construction of equations |
| 71 | A dissertation on continued fractions |
| 72 | Various observations about infinite series |
| 73 | The solution to a geometric problem about circles shaped as moons |
| 74 | On various methods for expressing the quadrature of a circle with verging numbers |
| 75 | Solution of a problem proposed in the Nova Acta Eruditorum in November, 1743 |
| 76 | New and correct tables for computing the location of the moon |
| 77 | New Principles of Gunnery |
| 78 | Essay on a better construction of a capstan |
| 79 | A problem of geometry proposed publicly by an anonymous geometer |
| 80 | Opuscula varii argumenti |
| 82 | Percussion and its true measurement |
| 83 | On several properties of the conic sections which intersect with an infinity of other curved lines |
| 84 | Observation by Leonhard Euler on sections 83 and following of the preceding book, concerning elastic curves |
| 85 | Solution to a catoptric problem proposed in this journal in September 1745 on page 523 |
| 86 | On the movement of bodies on movable surfaces |
| 87 | Astronomical table of the sun and the moon |
| 88 | A new theory of light and colors |
| 89 | On the running down of the motion of the planets |
| 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 |
| 93 | An inquiry into balances |
| 94 | On the movement of a boat with oars propelled through running waters |
| 95 | On differential equations which admit integration only in certain cases |
| 96 | On the most profitable application of simple as well as composite machines |
| 97 | On the attraction of spherico-elliptical bodies |
| 98 | The proofs of some arithmetic theorems |
| 99 | The solution to a certain problem proposed by the celebrated Daniel Bernoulli |
| 100 | On Amicable Numbers |
| 101 | Introduction to the Analysis of the Infinite, volume 1 |
| 103 | Physical Investigations on the tail of comets, the northern lights, and the zodiacal light |
| 104 | Memoir on the effect of the successive propagation of light in the appearance of the planets as well as the comets |
| 105 | Memoir on the Grand Equation of the Planets |
| 106 | Solution to the catoptric problem in Novis Actis Eruditorum Lipsiensibus proposed in November 1745 |
| 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. |
| 108 | A dissertation on an observed tendency of magents |
| 109 | Dissertation on Magnets |
| 110 | Naval Science, volume 1 |
| 111 | Naval Science, volume 2 |
| 112 | Studies on the movement of celestial bodies in general |
| 113 | Method for finding the true moments of both the new and the full moon |
| 114 | Method of finding the true geocenter of the moon by the obsertvation of the occulation of a fixed star |
| 115 | Method of determining the longitude of the observation site by observation of the occulations of fixed stars by the moon |
| 116 | Memoir on the force of oars |
| 117 | Reflections on the last eclipse of the sun from July 25, 1748 |
| 118 | On the perfection of objective lenses of telescopes |
| 119 | On vibrations of excited chords |
| 121 | Physical conjectures on the propogation of sound and light with other dissertations: on amicable numbers, on natural equations, and on the rectification of ellipses |
| 122 | On products created from infinite factors |
| 123 | Observations on continued fractions |
| 124 | On the determination of the gradient of heat and cold at each point and time of a region |
| 125 | Consideration of a progression suitable for finding the quadrature of a circle |
| 126 | On a new type of oscillation |
| 127 | An explanation of the phenomena which proceed in turn from the movement of light |
| 128 | An easy method for computing the natural and artificial sines and tangents of angles |
| 129 | Investigation of curves which produce evolutes similar to themselves |
| 130 | Considerations on certain series |
| 131 | An emmendation to astronomical tables of locating the geocenters of planets |
| 132 | Method 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 |
| 133 | On the surface of scalene cones and of other conic bodies |
| 134 | Theorems on divisors of numbers |
| 135 | Various geometric demonstrations |
| 136 | On the propagation of pulses in an elastic medium |
| 137 | Examination of a design for propelling a ship by an internal principle of motion |
| 138 | On the motion of the lunar nodes, and on the variation of their inclination to the ecliptic |
| 139 | To what degree the motion of the earth is perturbed by the moon, more accurately investigated |
| 140 | On the vibration of strings |
| 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 |
| 142 | On the atmosphere of the moon as proved by the last ringed eclipse of the sun |
| 143 | On the friction of solid bodies |
| 144 | On the reduction of the resistance of friction |
| 145 | Research into the largest and the smallest which are found in the action of forces |
| 146 | Reflection on some general laws of nature which are observed in the effects of random forces |
| 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 |
| 150 | Meditations on the question of determining the moment of time by observations |
| 151 | A physical conjecture on the propagation of sound and light |
| 152 | On amicable numbers |
| 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 |
| 154 | Observations on the rectification of ellipses |
| 155 | Excerpt from a letter of Herr Euler about the concept of asterisms on the celestial sphere |
| 156 | Opusculorum tomus III. continens novam theoriam magnetis ab illustr. academia regia scient: Parisina praemio condecoratam a. 1744. |
| 157 | On the extraction of roots from irrational quantities |
| 158 | Various analytical observations about combinations |
| 159 | On the oscillating motion of flexible bodies |
| 160 | On the descent of bodies over an unevenly inclined plane |
| 161 | On the movement of bodies over an uneven horizontal plane |
| 162 | A method for integrating rational differential forms involving one variable |
| 163 | An easier and more expedient method for integrating rational differential forms |
| 164 | Theorems about the divisors of numbers contained in the form paa ± qbb |
| 165 | On the motion of fluids arising from different degrees of heat |
| 166 | On the reduction of curved lines to the arcs of circles |
| 167 | On the solution of a most difficult problem proposed by Fermat |
| 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 |
| 172 | On the parallax of the moon, with respect to its elevation and azimuth, under the hypothesis of a spherical earth |
| 173 | New method of finding reciprocal algebraic trajectories |
| 174 | On the motion of flexible bodies |
| 175 | Discovery of an extraordinary law of numbers in relation to the sum of their divisors |
| 176 | Exposé 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 |
| 177 | Discovery of a new principle in Mechanics |
| 178 | Reflections of the different degrees of sunlight on other celestial bodies |
| 179 | Research concerning the effects of a hydraulic machine proposed by M. Segner, professor at Gottingen |
| 180 | Notice on the subject of Research on the precession of the equinoxes |
| 181 | Research on the origin of forces |
| 182 | Letter of Mr. Euler to M. Merian |
| 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 |
| 186 | Essay on the principle of least action, with an examination of the objections of M. Professor Koenig made against this principle |
| 187 | Theory of the motion of the moon which exhibits all its irregularities |
| 188 | Method of integrating differential equations of higher degrees, further developed |
| 189 | On the determination of series, or a new method for finding the general terms of series |
| 190 | Consideration of certain series which are gifted with particular properties |
| 191 | On the partitions of numbers |
| 192 | Solution of a problem of geometry |
| 193 | On the perturbation of the movement of planets from a figure not arising from a sphere |
| 194 | On machines in general |
| 195 | On the tautochrone motion of pendulums |
| 196 | Improvement of the magic lantern and solar microscope |
| 197 | Harmony existing between the general principles of rest and movement by M. de Maupertuis |
| 198 | On the principle of least action |
| 199 | Examination of the dissertation of Professor Koenig inserted into the Acts of Leipzig for the month of March 1751 |
| 200 | Essay concerning a metaphysical experiment on the general principle of equilibrium |
| 201 | Calculation of the probability in the game of Rencontre |
| 202 | On 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 |
| 203 | Research on a new method to raise water proposed by M. Mour |
| 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 |
| 205 | Geographic Atlas – Preface |
| 206 | On the motion of water in conduits |
| 207 | In depth explanation concerning different methods in which to raise water through pumps with the greatest effectiveness |
| 208 | Maxims for the most advantageous arrangement of machines that raise water by use of pumps. |
| 209 | Essay concerning the physical explanation of colors which are issued from extremely thin surfaces |
| 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 |
| 211 | Problema, ad cuius solutionem geometrae invitantur; theorema, ad cuius demonstrationem geometrae invitantur |
| 212 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 1 |
| 213 | Remarks on the preceeding memories of M. Bernoulli |
| 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 |
| 216 | Examination of a controversy on the law of refraction of rays of different colors with respect to the different transparent media through which they pass |
| 217 | Examination of the true curve that bodies which are airborne or in any other fluid |
| 218 | A letter from L. Euler to E. Pontoppidan, dated 11 May 1754 |
| 219 | Concerning the refraction of light while passing through the atmosphere and the different degrees dependent on heat as to the elaticity of the air |
| 220 | Reflections on a problem of geometry dealt with by certain geometers which nevertheless is impossible |
| 221 | Research into the physics of the different refrangibilities of light rays |
| 222 | A more complete theory of machines which are activated by their reaction to water |
| 223 | Concerning the variation of latitude of fixed stars and the obliquity of the ecliptic |
| 224 | Notice |
| 225 | General principles concerning the state of the equilibrium of fluids |
| 226 | General principles concerning the motion of fluids |
| 227 | Continuation into the research on the theory of the motion of fluids |
| 228 | On numbers which are the sum of two squares |
| 229 | On the construction of the best gears |
| 230 | Elements of the doctrine of solids |
| 231 | Proof of some of the properties of solid bodies enclosed by planes |
| 232 | On the movement of celestial bodies perturbed by any number of forces |
| 233 | Refined studies into the effect of windmills |
| 234 | Experiments to determine the refraction of all types of transparent liquors |
| 235 | On the action of saws |
| 236 | Explanation of certain paradoxes in integral calculus |
| 237 | Research concerning the declination of the magnetized needle |
| 238 | Concerning the strength of columns |
| 239 | General rules for the construction of telescopes and microscopes, using some general number of lenses. |
| 240 | Research into glasses with three lenses which represent inverted objects |
| 241 | Proof of a theorem of Fermat that every prime number of the form 4n+1 is the sum of two squares |
| 242 | Proof of a theorem of Fermat that every number whether whole or fraction is the sum of four or fewer squares |
| 243 | Observations on the sums of divisors |
| 244 | A demonstration of a theorem on the order observed in the sums of divisors |
| 245 | On a method analogous to that of Diophantus in the analysis of the infinites |
| 246 | A contribution to the calculations of sines |
| 247 | On divergent series |
| 248 | On the screw of Archimedes |
| 249 | On finding the best shape for gear teeth |
| 250 | A method for finding infinitely many isoperimetric curves predicated with a common property |
| 251 | On the integration of the differential equations (m dx)/√(1-x4) = (n dy)/√(1-y4) |
| 252 | Observations on the comparison of arcs of irrectifiable curves |
| 253 | On indeterminate problems which appear to be quite determinate |
| 254 | On the expression of integrals as factors |
| 255 | General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions |
| 256 | Example of the use of observation in pure mathematics |
| 257 | On friction of rotating bodies |
| 258 | Principles of the motion of fluids |
| 259 | On the motion and reaction of water flowing through moving tubes |
| 260 | Attempt at a theory of the friction of fluids |
| 261 | Example of another new methods for comparing transcendental quantities; on the comparison of the arcs of ellipses |
| 262 | Theorems about the remainders left by division by powers |
| 263 | An example of a new method for the quadrature and rectification of curves and of comparing other quantities which are transcendentally related to each other |
| 264 | Proof of a theorem and solution of a theorem proposed in the Acta Eruditorum of Leipzig |
| 265 | On differential equations of the second degree |
| 267 | Extract of a letter of M. Euler written to M. Duhamel, 3 February 1756 |
| 268 | Letter of Mr. Euler to Mr. de Lagrange |
| 269 | On the integration of differential equations |
| 270 | The 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 |
| 271 | Demonstration of a new method in the Theory of Arithmetic |
| 272 | A reinforcement of some arithmetic theorems, supported by several demonstrations |
| 273 | Consideration of formulas, of which the integral can be obtained by sections of arcs of cones |
| 274 | Construction of the differentio-differential equation Ay du2 + (B+Cu)du dy + (D+Eu+Fuu)ddy = 0, assuming the element du to be constant |
| 275 | Annotations to a certain passage of Descartes for finding the quadrature of the circle |
| 276 | Clarifications into fluid resistance |
| 277 | Principal theory of machines |
| 278 | On the motion and grinding of lenses while they are polished upon curved plates |
| 279 | On the resolution of formulas of squares of indeterminates by integral numbers |
| 280 | On progressions of arcs of circles, of which the accompanying tangents proceed by a certain law |
| 281 | A specimen of a singular algorithm |
| 282 | On the resolution of equations of any order |
| 283 | On very large prime numbers |
| 284 | On the resolution of the equation dy + ayy dx = bxm dx |
| 285 | Investigation of functions from a given condition of differentials |
| 286 | On the vibrating motion of a flexible wire, weighted with however many small particles |
| 287 | On the vibrating motion of unevenly thick strings |
| 288 | Thoughts on constructing ramparts/walls |
| 289 | Theory of the motion of solid or rigid bodies |
| 291 | Research into the science of mechanical bodies |
| 292 | On the movement of rotation of solid bodies around a variable axis |
| 293 | General remarks on the daily motion of the planets |
| 294 | Remarks by Mr. Euler on several passages which appeared in the third volume of mathematical works by Mr. d’Alembert |
| 295 | On the reduction of integral formulas for the rectification of the ellipse and hyperbola |
| 296 | The Elements of the Calculus of Variations |
| 297 | Explanation of the analytical method in the maxima and minima |
| 298 | On the notable advancement of the inverse method of tangents |
| 299 | Explanation of the tautochrone in a resistant medium |
| 300 | Demonstration of a Bernoullian theorem in which cycloids are ultimately produced from the evolution, continued to infinity, of any right-angled curve |
| 301 | De motu corporis ad duo centra virium fixa attracti |
| 302 | On the motion of vibrations in drums |
| 303 | Tentamen de sono campanarum |
| 304 | Considerationes de motu corporum coelestium |
| 305 | On the propagartion of sound |
| 306 | Supplement to the research on the propagation of sound |
| 307 | Continuation into the propagation of sound |
| 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 |
| 311 | Research into simple microscopes and the methods to perfect them |
| 312 | Research on microscopes with three lenses and the methods by which to make them |
| 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 |
| 315 | Concerning the true character of modern music |
| 316 | On three lens glasses which represent upright objects |
| 317 | Clarifications on the movement of vibrating strings |
| 318 | Research into the motion of unequally thick strings |
| 319 | Research into the integration of the equation (ddz/dt2)=aa(ddz/dx2)+(b/x)(dz/dx) + (c/xx)z |
| 320 | Research into a new type of construction of six lens glasses and their improvement |
| 321 | Observations concerning the integrals of formulas ∫ xp-1dx(1-xn)q/n-1 setting x=1 after integration |
| 322 | The use of discontinued functions in analysis |
| 323 | Concerning the use of a new algorithm to solve the Pell problem |
| 324 | Properties of triangles for which certain angles have a ratio between themselves |
| 325 | Easy solutions to some difficult geometric problems |
| 326 | Analytical observations |
| 327 | On the rectilinear motion of three bodies mutually attracted to each other |
| 328 | On the motion of a body attracted to two fixed centers of forces |
| 329 | On the appearance of the heavens observed through transparent spherical segments |
| 330 | Supplement on the shape of the teeth of wheels [gear teeth] |
| 331 | On the motion of fluids arising from different degrees of heat |
| 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 |
| 336 | On the motion of a rotating solid round a mobile axis |
| 337 | Problem: 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 |
| 338 | On the probability of series in the Genoese lottery |
| 339 | On the motion of a string which at the start has only been struck only in one area |
| 340 | Detailed clarifications concerning the generation and propagation of sound and on the formation of echo |
| 342 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 2 |
| 345 | On integrated equations of the type dx/√(A+Bx+Cx2+Dx3+Ex4) = dy/√(A+By+Cy2+Dy3+Ey4) |
| 346 | De arcubus curvarum aeque amplis earumque comparatione |
| 347 | More general development of formulas serving for the comparison of curves |
| 348 | Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi |
| 349 | Disquisition on the true law of refraction of rays of different colors |
| 350 | On a new type of microscope composed of six lenses |
| 351 | On a telescope made from four lenses and its perfection |
| 352 | Remarks on a beautiful relation between direct as well as reciprocal power series |
| 353 | Research into the confusion which exists in dioptic lenses caused by their aperture |
| 354 | Research into the methods to diminish or reduce the confusion caused by the opening of the lenses |
| 355 | New method to improve the objective lenses for glasses |
| 356 | Determination of the apparent field that is discovered by telescopes as well as by microscopes |
| 357 | General rules for the construction of telescopes and of microscopes |
| 358 | On the perfection of astronomic glasses which represent inverted objects |
| 359 | The manufacture of lenses composed of two different types of glass which does not present any confusion |
| 360 | The correct way to manufacture composes lenses which will reduce all confusion in the glasses |
| 361 | Reflections on the ways in which to examine the refraction of glass by the way of prisms |
| 362 | The necessary corrections to the theory of the magnetic declination which was proposed in Volume XIII of the Memoires |
| 363 | Notebook concerning a general theory of dioptrics |
| 366 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 3 |
| 367 | Optics, part 1 |
| 368 | On a hyperbolic curve expressed by this equation y = 1*2*3*…*x |
| 369 | How very large numbers are to be tested for whether they are prime or not |
| 370 | A new criteria for acquiring the imaginary roots of equations |
| 371 | Considerations on completing the theory of the motion of the moon and especially of its variation |
| 372 | Note of certain precautions to be taken in the investigation of the inequalities by which the heavenly bodies are perturbed in their motion |
| 373 | More accurate investigation of the phenomena which can be produced in the diurnal motion of the earth by celestial forces |
| 374 | On the equilibrium and motion of bodies connected by flexible curves |
| 375 | First section on the state of equilibrium of fluids |
| 376 | Considerations on the difficulties that one encounters during the manufacture of objective lenses |
| 377 | Research into reflective telescopes and their perfection |
| 378 | Research on another construction of reflecting telescopes |
| 379 | Concerning the confusion which exists in dioptical instruments due to the diverse refrangibility of light rays |
| 380 | Concerning the new English glasses of Mr. Dolland and on the principle on which it is based |
| 381 | On the advantages of telescopic glasses built with two lenses |
| 382 | Remarks on the effect of friction on equilibrium |
| 383 | Methods to apply for improving the degree of perfection in the manufacture of telescopic lenses |
| 384 | Research on the inequalities of Jupiter and Saturn |
| 385 | Foundations of Integral Calculus, volume 3 |
| 386 | Optics, part 2 |
| 387 | Complete instruction in algebra, book 1 |
| 388 | Complete instruction in algebra, book 2 |
| 390 | (Considerations of orthogonal trajectories) |
| 391 | On double integral formulas |
| 392 | Development of a notable paradox concerning the equality of surfaces |
| 393 | On the sum of series involving the Bernoulli numbers |
| 394 | On the partition of numbers into a number of parts of a given type |
| 395 | On finding however many mean proportionals without regard to extraction of roots |
| 398 | New method to determine the perturbations during the motion of heavenly bodies caused by their mutual attraction |
| 399 | Reflections on the different ways that one can describe the movement of the moon |
| 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 |
| 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? |
| 419 | On solids whose (entire) surface can be unfolded onto a plane |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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. |
| 486 | Answer to the question proposed by the Paris Academy for 1772 |
| 487 | Thoughts by Mr. L. Euler concerning new experiments in optics transmitted to the Academy by Mr. Wilson |
| 488 | Observations on the foregoing dissertation of Bernoulli |
| 489 | On unravelling exponential formulas |
| 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 | De figura quam ventus fluido stagnanti inducere valet |
| 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 |
| 500 | On 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 |
| 501 | Considerations about brachistochrones |
| 502 | On the effects of refraction during terrestrial observations |
| 503 | De motu oscillatorio penduli cuiuscunque, dum arcus datae amplitudinis absolvit |
| 504 | On the Theory of the Moon which is to be carried to a higher level of perfection |
| 505 | De 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 |
| 507 | On the infinity of infinities of orders of the infinitely large and infinitely small |
| 508 | The determination of the loads which columns are strong enough to bear |
| 509 | An examination of an outstanding paradox occurring in the theory of columns |
| 510 | De altitudine columnarum sub proprio pondere corruentium |
| 511 | Thoughts concerning the Earth’s motional inequalities caused by Venus’ action, accompanied with a table of the corrections of Earth’s position |
| 512 | Investigatio perturbationum quae in motu terrae ab actione Veneris producunter: cum tabula perturbationum istarum |
| 513 | On triangular curves |
| 514 | On the measure of solid angles |
| 515 | De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur |
| 516 | De motu oscillatorio duorum corporum ex filo super trochleas traducto suspensorum |
| 517 | On a certain problem in mechanics, obvious enough, but with a most difficult solution |
| 518 | Solutio gemina problematis, quo motus corporis, filo alicubi alligati, super plano horizontali quaeritur |
| 519 | New method to determine the motion of planets |
| 520 | Essay of the theory of resistance that a prow of a ship experiences throughout its motion |
| 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 |
| 524 | A universal spherical trigonometry, derived briefly and from first principles |
| 525 | De motu oscillatorio mixto plurium pendulorum ex eodem corpore mobili suspensorum |
| 526 | Investigatio motuum, quibus laminae et virgae elasticae contremiscunt |
| 527 | A conjecture about the nature of air, by which are to be explained the phenomenon which have been observed in the atmosphere |
| 528 | An annotation to the preceding dissertation |
| 529 | A theory of parallaxes, accommodating the spheroid shape of the Earth |
| 530 | Investigations on a new type of magic square |
| 531 | Brief analytical works, volume 1 |
| 532 | On the remarkable properties of a series of Lambert and others |
| 533 | On the oscillating motion derived from a tense hanging thread |
| 534 | Elucidations about several rather difficult cases of equilibrium |
| 535 | Determinatio omnium motuum, quos chorda tensa et uniformiter crassa recipere potest |
| 536 | On the properties of triangles in mechanics |
| 537 | On the figure of elastic curves against the objections of the illustrious d’Alembert |
| 538 | Necessary cautions in the determination of the motion of planets which are to be observed |
| 539 | A supplement to the calculation of integrals for the calculation of irrational formulas |
| 540 | A new method for resolving all rational fractions into simpler fractions |
| 541 | The expansion of the infinite product (1-x)(1-xx)(1-x3)(1-x4)(1-x5) etc. into a single series |
| 542 | On the remarkable properties of the pentagonal numbers |
| 543 | Problematis cuiusdam Pappi Alexandrini constructio |
| 544 | De motu libero plurium corporum filis colligatorum super plano horizontali |
| 545 | De vi fluminis ad naves sursum trahendas applicanda |
| 546 | De statu aequilibrii maris a viribus solis et lunae sollicitati. |
| 547 | Simple determination of the orbit of a comet, when it is possible to observe its transit across the ecliptic twice |
| 548 | De variis motuum generibus, qui in satellitibus planetarum locum habere possunt. |
| 549 | De motibus maxime irregularibus, qui in systemate mundano locum habere possent, una cum methodo hujusmodi motus per temporis spatium quantumvis magnum prosequendi. |
| 550 | On series in which the product of two consecutive terms make a given progression |
| 551 | Various methods for inquiring into the innate characters of series |
| 552 | Observations about the division of squares by prime numbers |
| 553 | Analytical observations |
| 554 | A more exact disquisition about the residues remaining from the division of squares and of higher powers by prime numbers |
| 555 | An examination of the use of interpolating methods in the doctrine of series |
| 556 | On the criteria of whether equation fxx + gyy = hxx admits a resolution or not |
| 557 | De quibusdam eximiis proprietatibus circa divisores potestatum occurrentibus |
| 558 | Proposita quacunque protressione ab unitate incipiente, quaeritur quot eius terminos a dminimum addi oporteat, ut omnes numeri producantur |
| 559 | New assistance for solving the formula axx + 1 = yy |
| 560 | Miscellaneous analyses |
| 561 | Various observations about angles proceeding in geometric progression |
| 562 | On how sines and cosines of multiplied angles may be expressed by products |
| 563 | On the smallest ellipse which is to circumsrcibe a given rectilinear parallelogram |
| 564 | Speculations about certain outstanding properties of numbers |
| 565 | On highly transcendental quantities, which may not be expressed in any way by integral formulas |
| 566 | De inductione ad plenam certitudinem evehenda |
| 567 | Dilucidationes de motu chordarum inaequaliter crassarum |
| 568 | De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Remota frictione |
| 569 | De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Habita frictionis ratione |
| 570 | On finding longitude of a place by observing the distance between the moon and a known fixed star |
| 571 | De eclipsibus solaribus in superficie terrae per proiectionem repraesentandis. |
| 572 | Nova methodus integrandi formulas differentiales rationales sine subsidio quantitatum imaginariarum |
| 573 | De duplici genesi tam epicycloidum quam hypocycloidum |
| 574 | De curvis rectificabilibus in superficie coni recti ducendis |
| 575 | De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt |
| 576 | De oscillationibus minimis funis libere suspensi |
| 577 | De perturbatione motus chordarum ab earum pondere oriunda |
| 578 | On the disturbance of motion concerning planets and comets |
| 579 | Caculation 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 |
| 580 | Brief analytical works, volume 2 |
| 581 | A 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. |
| 582 | The fruitful development of a relation which may be established between the arcs of conic sections |
| 583 | De numero memorabili in summatione progressionis harmonicae naturalis occurrente |
| 584 | De insignibus proprietatibus unciarum binomii ad uncias quorumvis polynomiorum extensis |
| 585 | De effectu frictionis in motu volutorio |
| 586 | Considerations about a theorem of Fermat on the resolution of numbers into polygonal numbers |
| 587 | An observation on several theorems of the illustrious de la Grange |
| 588 | An investigation of the integral formula ∫ (xm-1 dx)/(1+xk)n in the case in which after integration it is set x = ∞ |
| 589 | An investigation of the value of the integral ∫ (xm-1 dx)/(1-2xkcosθ+x2k) the term to be extended from x = 0 to x = ∞ |
| 590 | Certain theorems in analysis, of which a demonstration is thus far desired |
| 591 | On the relation between three and more quantities which are to be instituted |
| 592 | On the resolution of transcendental fractions into infinitely many simple fractions |
| 593 | On the transformation of series into continued fractions, where at once this not mediocre theory is enlarged |
| 594 | A 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 |
| 595 | Summatio fractionis continuae cuius indices progressionem arithmeticam constituunt dum numeratores omnes sunt unitates ubi simul resolutio aequationis Riccatianae per huiusmodi fractiones docetur |
| 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 |
| 597 | A new and most easy method for summing series of reciprocals of powers |
| 598 | De insigni promotione scientiae numerorum |
| 599 | Solution 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 |
| 600 | The solution of certain difficult questions in the calculus of probabilities |
| 601 | De symptomatibus quatuor punctorum, in eodem plano sitorum |
| 602 | Methodus facilis omnia symptomata linearum curvarum non in eodem plano sitarum investigandi |
| 603 | De descensu baculi super hypomochlio cylindro fixo delabentis |
| 604 | On rectilinear and oblique reciprocal trajectories |
| 605 | On the remarkable properties of the elastic curves under the equation y = ∫ (xx dx)/√(1-x4) |
| 606 | Speculations concerning the integral formula ∫ (xndx)/√(aa-2bx+cxx), where at once occur exceptional observations about continued fractions |
| 607 | De motu globi circa axem obliquum quemcunque gyrantis et super plano horizontali incedentis |
| 608 | Accuratior evolutio formularum pro filorum flexibilium aequilibrio et motu inventarum |
| 609 | Considerations about rectilinear and oblique trajectories |
| 610 | New demonstrations about the divisors of numbers of the form xx + nyy |
| 611 | Investigatio curvarum quae similes sint suis evolutis vel primis vel secundis vel tertiis vel adeo ordinis cuiuscunque |
| 612 | De motu globi heterogenei super plano horizontali, una cum dilucidationibus necessariis super motu vacillatorio |
| 613 | Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus |
| 614 | Commentary on tractrix curves |
| 615 | De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis |
| 616 | On the transformation of the divergent series 1 – mx + m(m+n)x2 – m(m+n)(m+2n)x3 + etc. into a continued fraction |
| 617 | On the summation of series, in which the signs of the terms alternate |
| 618 | Consideratio motus singularis, qui in filo perfecte flexili locum habere potest |
| 619 | Enodatio difficultatis super figura terrae a vi centrifuga oriunda. |
| 620 | An 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 = ∞ |
| 621 | On the greatest use of the calculus of imaginaries in analysis |
| 622 | Specimen singulare analyseos infinitorum indeterminatae |
| 623 | De lineis rectificabilibus in superficie sphaeroidica quacunque geometrice ducendis |
| 624 | De superficie coni scaleni, ubi imprimis intentes difficultates, quae in hac investigatione occurrunt, perpenduntur |
| 625 | De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis |
| 626 | On the movement of three bodies mutually attracted above a straight line |
| 627 | Solutio problematis mechanici |
| 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 |
| 629 | The expansion of the integral formula ∫ dx(1/(1-x) + 1/(lx)) with the term extended from x = 0 to x = 1 |
| 630 | Uberior explicatio methodi singularis nuper expositae integralia alias maxime abscondita investigandi |
| 631 | An 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 |
| 632 | On 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 |
| 633 | De binis curvis algebraicis inveniendis, quarum arcus indefinite inter se sint aequales |
| 634 | De motu oscillatorio tabulae suspensae et a vento agitatae |
| 635 | Innumera theoremata circa formulas integrales, quorum demonstratio vires analyseos superare videatur |
| 636 | On the multiplication of angles which are to be obtained by factors |
| 637 | A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents |
| 638 | On innumerable algebraic curves, of which the longitude is able to be measured by parabolic arcs |
| 639 | On innumerable algebraic curves, of which the longitude is able to be measured by elliptical arcs |
| 640 | Comparatio valorum formulae integralis ∫ (xp-1 dx)/(n√((1-xn)n–q)) a termino x = 0 usque ad x = 1 extensae |
| 641 | De motu quodam maxime memorabili, satis quidem simplici, at solutu difficillimo |
| 642 | On a singular rule for differentiating and integrating, which occurs in the sums of series |
| 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 |
| 645 | On algebraic curves, of which the longitudes are expressed by the integral formula ∫ (vm-1 dv)/√(1-v2n) |
| 646 | De duabus pluribusve curvis algebraicis in quibus si a terminis fixis aequales arcus abscindantur eorum amplitudines datam inter se teneant rationem |
| 647 | De methodo tangentium inversa ad theoriam solidorum translata |
| 648 | An easy solution of a problem, in which a circle is searched for, given three circles tangent to it |
| 649 | De motu oscillatorio penduli circa axem cylindricum plano horizontali incumbentem |
| 650 | De formulis differentialibus quae per duas pluresve quantitates datas multiplicatae fiant integrabiles |
| 651 | Four most noteworthy theorems on the calculation of an integral |
| 652 | On the general term of hypergeometric series |
| 653 | De iterata integratione formularum integralium, dum aliquis exponens pro variabili assumitur |
| 654 | Methodus facilis investigandi radium osculi ex principio maximorum et minimorum petita |
| 655 | General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth |
| 656 | On most memorable integrations arising from the calculation of imaginaries |
| 657 | A 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)) |
| 658 | De momentis virium respectu axis cuiuscunque inveniendis; ubi plura insignia symptomata circa binas rectas, non in eodem plano sitas, explicantur |
| 659 | Methodus facilis omnium virium momenta respectu axis cuiuscunque determinandi |
| 660 | Foundations of Integral Calculus, Volume 4 |
| 661 | Several considerations about hypergeometric series |
| 662 | On 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 |
| 663 | Plenior expositio serierum illarum memoragilium, quae ex unciis potestatum binomii formantur |
| 664 | Analytical exercises |
| 665 | The evolution of a problem whose analytic solution is most difficult, while the synthetic solution for it is obvious |
| 666 | Problema geometricum ob singularia symptomata imprimis memorabile |
| 667 | De curvis hyperbolicis quae intra suas assymtotas spatium finitum includunt |
| 668 | On the integration of the formula (dx √(1+x4))/(1-x4) and of others of the same type by logarithms and circular arcs |
| 669 | Memorabile genus formularum differentialium maxime irrationalium quas tamen ad rationalitatem perducere licet |
| 670 | De resolutione formulae integralis ∫ (xm-1 dx)(Δ + xn)λ in seriem semper convergentem, ubi simul plura insignia artificia circa serierum summationem explicantur |
| 671 | De formulis differentialibus angularibus maxime irrationalibus, quas tamen per logarithmos et arcus circulares integrare licet |
| 672 | A memorable theorem about the integral formula ∫ (dφ cos(λφ))/(1+aa-2acos(φ))n+1 |
| 673 | A conjectural disquisition about the integral formula ∫ (dφcos(iφ))/(α+βcos(φ))n |
| 674 | Demonstratio theorematis insignis per coniecturam eruti circa intagrationem formulae ∫ (dφ cos(iφ))/(1+aa-2acos(φ))n+1 |
| 675 | On the values of integrals where the variable term is extended x = 0 all the way to x = ∞ |
| 676 | Methodus succinctior comparationes quantitatum transcendentium in forma ∫ (P dz)/√(A + 2Bz + Czz + 2Dz3 + Ez4) contentarum inveniendi |
| 677 | Special methods for resolving differential equations of the second degree |
| 678 | A new method for investigating all cases in which the differential equation ddy(1-axx) – bx dx dy – cy dx2 = 0 is permitted to resolve |
| 679 | De formulis integralibus implicatis earumque evolutione et transformatione |
| 680 | De aequationibus differentialibus cuiuscunque gradus quae denuo differentiatae integrari possunt |
| 681 | Specimen aequationum differentialium indefiniti gradus earumque integrationis |
| 682 | On the pressure of a table weighted by a weight on a surface. From the papers of the blessed Leonhard Euler extracted by Jakob Bernoulli. |
| 683 | On a singular type of Diophantine questions and a most recondite method by which they are to be resolved |
| 684 | On 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. |
| 685 | An analytical exercise, where in particular a most general summation of series is given |
| 686 | Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted |
| 687 | De insignibus proprietatibus formularum integralium praeter binas variabiles etiam earum differentialia cuiuscunque ordinis involventium |
| 688 | A most abstruse specimen of integral contained in the formula ∫ dx/((1+x)*4√(2xx-1)) |
| 689 | Integratio formulae differentialis maxime irrationalis, quam tamen per logarithmos et arcus circulares expedire licet |
| 690 | The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*4√(1+6zz+z4)) by logarithms and circular arcs |
| 691 | Problema geometricum quo inter omnes ellipses quae per data quatuor puncta traduci possunt ea quaeritur quae habet aream minimam |
| 692 | Solutio problematis maxime curiosi quo inter omnes ellipses quae circa datum triangulum circumscribi possunt ea quaeritur cuius area sit omnium minima |
| 693 | On the center of similarity |
| 694 | Later paper on formulas of imaginary integrals |
| 695 | A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*3√(1±3zz)) |
| 696 | On the cases in which the form x4 + kxxyy + y4 is permitted to be reduced to a square |
| 697 | Investigatio superficierum quarum normales ad datum planum productae sint omnes inter se aequales |
| 698 | Several speculations about the area of spherical triangles |
| 699 | Inquiring on whether or not the number 100009 is prime |
| 700 | On differential equations of the second degree which admit integration |
| 701 | Formae generales differentialium, quae, etsi nulla substitutione rationales reddi possunt. tamen integrationem per logarithmos et arcus circulares admittunt |
| 702 | De novo genere quaestionum arithmeticarum pro quibus solvendis certa methodus adhuc desideratur |
| 703 | An 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 |
| 704 | Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus |
| 705 | Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae |
| 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 |
| 707 | On the outstanding use of the calculation of imaginations in the calculation of an integral |
| 708 | On forms of the type mxx + nyy for exploring prime numbers by idoneals of them with remarkable properties |
| 709 | On the expansion of the power of any polynomial 1 + x + x2 + x3 + x4 + etc. |
| 711 | A new and easy method for expressing for all algebraic equations not only their roots but also the powers of them by constructing series |
| 712 | De corporibus cylindricis incurvatis |
| 713 | An investigation of a triangle in which the distances of the angles from the center of gravity of it may be expressed rationally |
| 714 | Exempla quarundam memorabilium aequationum differentialium, quas adeo algebraice integrare licet, etiamsi nulla via pateat variabiles a se invicem separandi |
| 715 | On various ways of examining very large numbers, for whether or not they are primes |
| 716 | The resolution of the Diophantine formula ab(maa+nbb) = cd(mcc+ndd) by rational numbers |
| 717 | Solution to a problem of mechanics |
| 718 | An easy method of finding several rather large prime numbers |
| 719 | A more general method by which all adequately large numbers may be scrutinized for whether or not they are prime |
| 720 | Special observations about linear differential equations |
| 721 | De integrationibus difficillimis, quarum integralia tamen aliunde exhiberi possunt |
| 722 | Analytical disquisitions on the expansion of the trinomial power (1+x+xx)n |
| 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 |
| 726 | A demonstration of a notable theorem of numbers a twelfth part of binomial powers |
| 727 | A more accurate treatment of the problem of drawing the shortest line on a surface |
| 728 | On the resolution of composite fractions into simpler ones |
| 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 |
| 733 | Solutio facilis problematis, quo quaeritur sphaera, quae datas quatuor sphaeras utcunque dispositas contingat |
| 734 | The integration of the differential equation dy + yydx = (A dx)/(a+2bx+cxx)2 |
| 735 | On an outstanding paradox, which occurs in the analysis of maximums and minimums |
| 736 | On the summation of series contained in the form a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc. |
| 737 | De transformatione functionum duas variabiles involventium dum earum loco aliae binae variabiles introducuntur |
| 738 | The solution of a curious question in the scene of combinations |
| 739 | An easy rule for Diophantine problems which are to be resolved quickly by integral numbers |
| 740 | De lineis curvis non in eodem plano sitis, quae maximi minimive proprietate sunt praeditae |
| 741 | Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi |
| 742 | Observations about continued fractions contained in the form S = n/(1+(n+1)/(2+(n+2)/(3+(n+3)/(4+etc.)))) |
| 743 | De serie maxime memorabili, qua potestas binomialis quaecunque exprimi potest |
| 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 |
| 747 | On remarkable series, by which the sines and cosines of multiplied angles may be expressed |
| 748 | Investigatio quadrilateri, in quo singularum angulorum sinus datam inter se teneant rationem, ubi artificia prorsus singularia in Analysi Diophantea occurrunt |
| 749 | About geometry and spheres |
| 750 | A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers |
| 751 | Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi |
| 752 | De integralibus quibusdam inventu difficillimis |
| 753 | Solution succincta et elegans problematis, quo quaeruntur tres numeri tales, ut tam summae quam differentiae binorum sint quadrata |
| 754 | On a problem of geometry resolved by Diophantine analysis |
| 755 | On cases for which the formula x4 + mxxyy + y4 can be reduced to a square |
| 756 | Solution to some curious problems of mechanics |
| 757 | On the problem of orthogonal trajectories, translated to surfaces |
| 758 | De binis formulis speciei xx + myy et xx + nyy inter se concordibus et discordibus |
| 759 | A more accurate investigation into brachistochrones |
| 760 | De vera brachystochrona seu linea celerrimi descensus in medio resistente |
| 761 | De brachystochrona in medio resistente, dum corpus ad centrum virium utunque attrahitur |
| 762 | Unpublished letter from Euler to Lagrange |
| 763 | De tribus pluribusve numeris inveniendis, quorum summa sit quadratum, quadratorum vero summa biquadratum |
| 764 | An 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 |
| 765 | De problemate curvarum synchronarum, eiusque imprimis inverso |
| 766 | Methodus nova et generalis problema synchronarum inversum aliaque eiusdem generis resolvendi |
| 767 | De curvis quarum radii osculi tenent rationem duplicatam distantiae a puncto fixo earumque mirabilibus proprietatibus |
| 768 | De unciis potestatum binomii earumque interpolatione |
| 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 |
| 770 | Enodatio maximi paradoxi, in problemate quodam mechanico occurentis |
| 771 | Solutio trium problematum difficiliorum ad methodum tangentium inversam pertinentium |
| 772 | De insigni promotione Analysis Diophantaeae |
| 773 | A solution of a most difficult problem, in which the two forms aaxx + bbyy et aayy + bbxx must be rendered into squares |
| 774 | An investigation of two numbers of the form xy(x4–y4), of which the product and the quotient will be a square |
| 775 | On two numbers, of which the sum when increased or decreased by the square of one of them produces a square |
| 776 | Elucidations about two sums of pairs of biquadratics, which are mutually equal |
| 777 | On the resolution of the equation 0 = a + bx + cy + dxx + exy + fyy + gxxy + hyy + ixxyy by rational numbers |
| 778 | A new and easy method for reducing cubic and biquadratic forms to squares |
| 779 | Solutio problematis ad analysin infinitorum indeterminatorum referendi |
| 780 | De infinitis curvis algebraicis, quarum longitudo indefinita arcui elliptico aequatur |
| 781 | De infinitis curvis algebraicis, quarum longitudo arcui parabolico aequatur |
| 782 | De binis curvis algebraicis eadem rectificatione gaudentibus |
| 783 | On algebraic curves, all of whose arcs may be measured by circular arcs |
| 784 | Solution to a very difficult analytical problem |
| 785 | Integration of a remarkable type of differential equation in analytical functions with two variables |
| 787 | Solution of a problem proposed in the Leipzig Acts in 1745 |
| 788 | Letters of L. Euler and Chr. Goldbach 1729-1763 |
| 789 | A few lines from a letter of L. Euler to Albrecht von Haller, from 4 July 1744 |
| 790 | Commentary on the use of sublime mathematics |
| 792 | Tractatus de numerorum doctrina capita sedecim, quae supersunt |
| 793 | Thoughts concerning Diophantine analysis |
| 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 |
| 798 | On amicable numbers |
| 799 | A 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 |
| 800 | A letter from L. Euler to Christoph Jezler, dated 4 May 1765 |
| 801 | Three letters of Euler to Frederick the Great in 1743 |
| 802 | Einige Zeilen aus Briefen von L. Euler an Johannes Schorndorf vom 27 April 1743 und vom 26 Mai 1750 |
| 803 | Vierzehn Briefe oder Auszuge aus Briefen von L. Euler an W.J.G. Karsten 1758-1765 |
| 804 | Two letters of Euler to Bulffinger in 1738 |
| 805 | Posthumous works in mathematics and physics |
| 806 | Arithmetical fragments taken from the mathematical day book |
| 807 | On the logarithms of negative and imaginary numbers |
| 808 | An algebraic problem of finding four numbers with the sum of the three others |
| 809 | Series maxime idoneae pro circuli quadratura proxime invenienda |
| 810 | Enodatio insignis cuiusdam paradoxi circa multiplicationem angulorum observati |
| 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 |
| 814 | Foundations of Differential Calculus, volume 3 |
| 815 | Solution of problems from the theory of maxima and minima |
| 816 | Thoughts on certain integral formulas for which the values can be expressed under certain circumstances by the squaring of the circle |
| 817 | On curved lines, the rectification of which is measured by given quadratures |
| 818 | On the comparison of irrectifiable curved arcs |
| 819 | Continuation of some fragments taken from the Mathematics day book |
| 820 | Six letters to Nicholas Bernoulli II of Basel, dated 1742 to 1745 |
| 821 | Two letters to Frederick II, King of Prussia, sent in the years 1749 and 1763 |
| 822 | Eighteen letters to Lagrange from 1755 to 1775 |
| 823 | Statics |
| 824 | Vera vires existimandi ratio |
| 825 | De motu corporum circa punctum fixum mobilium |
| 826 | On the motion of a body on a moving surface |
| 827 | De motu corporum in tubo rectilineo mobili circa axem fixum, per ipsum tubum transeuntem |
| 828 | Dissertation on the motion of enclosed bodies in a rigid tube mobile around a fixed axis |
| 829 | De motu corporum in tubis circa punctum fixum mobilibus |
| 830 | Recensio litterarum a Cl. D. Bernoullio basilea die 26. Oct. 1735 ad me datarum, una cum annotationibus meis |
| 831 | De oscillationibus annulorum elasticorum |
| 832 | Von der Kraft der Rammen, Pfahle einzuschlagen |
| 833 | To determine the effect of a hydraulic machine invented by Mr. Segner, a Professor at Gottingen |
| 834 | Astronomia mechanica adjecta Digressione de cometa A. 1757 |
| 835 | Solutio duorum problematum, Astronomiam mechanicam spectantium |
| 836 | New astronomical tables for calculating the position of the sun |
| 837 | De emendatione tabularum lunarium per observationes eclipsium lunae |
| 838 | Tria capita ex opere quodam majori inedito de theoria lunae |
| 839 | De atmosphaera lunae ex eclipsi colis annulari evicta |
| 840 | De motu cometarum in orbitis parabolicis, solem in foco habentibus |
| 841 | Research into the inequalities caused by planetary motion by random forces |
| 842 | An Introduction to Natural Science |
| 843 | Constructio manometri densitatem aeris quovis tempore accurate monstrantis |
| 844 | General theory of dioptrics |
| 845 | Seven chapters of a work on dioptrics |
| 846 | Research to serve for the perfection of glasses |
| 847 | De amplificatione campi apparentis in telescopiis |
| 848 | Concerning the construction of microscopes |
| 849 | Reflections on the determination of compass readings |
| 850 | Research on the discovery of the currents of the sea |
| 851 | Recensio Dissertationis de ventis |
| 852 | Thoughts on the formation of the voice |
| 853 | Meditation on experiments made recently on the firing of a cannon |
| 854 | Several pieces about monads |
| 855 | Determination of the prinicples of motion of blood through arteries |
| 856 | Fragments from the mathematical day book |
| 857 | Three unpublished from Euler to Johann Bernoulli I, 1729-1737 |
| 858 | Unpublished letters from Euler to d’Alembert |
| 860 | Fourteen letters from Euler to P. L. M. de Maupertuis, 1752-1759 |
| 861 | Extracts of letters from Euler to Johann Bernoulli I, 1739-1740 |
| 862 | Extracts of letters from Euler to Johann Bernoulli I, 1728-1729 |
| 863 | The correspondence between Leonhard Euler and Johann I Bernoulli, 1727-1740 |
| 864 | The correspondence between Leonhard Euler and Daniel Bernoulli |
| 865 | Several lines of a letter from Euler to the “Royal Society” dated October 21/November 1, 1768 |
| 866 | Letter from Euler to J. d’Alembert from February 15, 1748 |