The Kepler problem from Newton to Johann Bernoulli.

Newton solved what was called at the time "the direct Kepler problem": given a curve (e.g., an ellipse) and the center of attraction (e.g., the focus), what is the law of attraction, if Kepler's second law holds? The "inverse problem", the determination of all possible orbit solutions for a given central force field, was systematically treated later, first by Jacob Hermann, and then thoroughly and completely by Johann Bernoulli. This paper traces the history of work on the problem and of the accompanying scientific controversies until the time of Johann Bernoulli and his pupil Leonhard Euler.