by Daniel Bernoulli, who won a prize for it from the Paris Academy in 1734. When three mutually attracting bodies were considered, progress appeared to be much more difficult. Clairaut wrote:

I have deduced the equations given here at the first moment, but I only applied few efforts to their solution, since they appeared to me little tractable. Perhaps they are more promising to others. I have given them up and have taken to using the method of approximations.

and, looking back on his efforts at finding a solution, Euler wrote:

As often as I have tried these forty years to derive the theory and motion of the moon from the principles of gravitation, there always arose so many difficulties that I am compelled to break off my work and latest researches. The problem reduces to three differential equations of the second degree, which not only cannot be

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