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 |
166 | On the reduction of curved lines to the arcs of circles |
167 | On the solution of a most difficult problem proposed by Fermat |
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 |
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 |
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-x^{4}) = (n dy)/√(1-y^{4}) |
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 |
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 du^{2} + (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 = bx^{m} 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 |
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 |
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 |
345 | On integrated equations of the type dx/√(A+Bx+Cx^{2}+Dx^{3}+Ex^{4}) = dy/√(A+By+Cy^{2}+Dy^{3}+Ey^{4}) |
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 |
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 |
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 |
396 | Section two of Principles of Fluid Motion |
397 | Exposition 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 |
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 |
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 |
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)(zdx^{2}/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 |
447 | The summation of the progressions sin(φ^{λ}) + sin(2φ^{λ}) + sin(3φ^{λ}) + ... + sin(nφ^{λ}); cos(φ^{λ}) + cos(2φ^{λ}) + cos(3φ^{λ}) + ... + cos(nφ^{λ}). |
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 Ax^{2} + 2Bxy + Cy^{2} + 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 |
462 | On the value of the integral formula ∫ (z^{m-1} ± z^{n-m-1})/(1 ± z^{n}) dz in the case in which after integration it is put z = 1 |
463 | On the value of the integral formula ∫ (z^{λ-ω} ± z^{λ+ω})/(1 ± z^{2λ})(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. |