Commentarii Academiae Scientiarum Petropolitanae

Original Titles
English Titles

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
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
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
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
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
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
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
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